I can't really afford private lessons but I do it!! (Yeah, dancing can make you a bit crazy; I'm very frugal so I cut back elsewhere and as it's so good for my emotional and physical health, hubby supports it). We did group for almost two years, last summer I started private. I was only going to take 3-4 lessons but my understanding of dance and skill level increased so much that I'd have a very hard time dropping them. If things were really tight, I'd cut back a bit, but that's it. We take group for the social aspect and we do learn some things, but it's night and day from a private lesson. I read something like 1 private equals 6 group lessons.
I agree about the goals, I never thought I'd perform, but when my instructor suggested doing a showcase, I realized it would help me focus and have set goals. Now I'm preparing for an actual competition. I NEVER thought I'd do that. I focus on smooth, but enjoy rhythm too. My showcase was Rhumba, my comp will be Tango, Fox Trot and Waltz. If you're serious, private lessons are necessary.
But what do you mean by "serious training" and "amateur level"? Have you been competing? If so, how's that been going? Or do you mean you enjoy social dancing? I started dancing in my late 50's so I'll never be at a high level, but I keep improving. I'd actually say I can see the difference from the start of a class to the end. That's what a good teacher and real commitment can do. Again, it's incremental, but every things builds to the next thing.